Exam1_Answers_06c

Exam1_Answers_06c - E SE 301 Engineering P robability F i...

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Unformatted text preview: E SE 301 Engineering P robability F i rst Exam Answers, October 12, 2006 1. Desired probability is no more than 0.67 using Markov’s Inequality w hich we haven’t come to yet. 2. 3 over (49 choose 6) 3. The three conditional probabilities are 14/41, 12/41, and 15/41. 4. Let alpha = P(guilt). Then P(jury correct) = alpha * P(jury decides guilty |guil ty) + (1-alpha) * P(jury decides innocent | i nnocence). The t wo probabilities are binomial summations: P(jury decides guilty | guilty) = sum(i=8 to 12)(12 choose i) theta^i(1-theta)^(12-i) and P(jury decides innocent | innocence) = sum(i=5 to 12)(12 choose i) theta^i(1theta)^(12-i). 5. Reduces to (4 *39! *13!)/52! 6. 3/64 7. Requires an analytical derivation. 8. 0.4^4*(1+4*.6) + 0.6^4*(1+4*.4) = .424 9. ¾ but this uses Chebyshev’s Inequality which we will not get to until l ater in the course. 10. Need an analytical demonstration that the geometric rv is memoryless. ...
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This note was uploaded on 03/02/2011 for the course ESE 301 taught by Professor Keenan during the Fall '10 term at UPenn.

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